Finite Group Databasebeta

← C151×#19005 #50323930

Subgroups — C151×#19005 #50323930

Order 38656.

820 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3531×C151C211yesmaximal, characteristic
2#3239×C151C212yesmaximal, complemented
3#3139×C151C211yesmaximal, characteristic, complemented
4#1664×C151C214yesmaximal, complemented
5#1663×C151C212yesmaximal, complemented
6#1662×C151C212yesmaximal, complemented
7#1537×C151C211yesmaximal, characteristic, complemented
8#1529×C151C212yesmaximal, complemented
9#564×C151C2211yescharacteristic
10#563×C151—22no—
11#563×C151—22no—
12#563×C151C2212yes—
13#562×C151—22no—
14#562×C151C2211yescharacteristic
15#533×C151—22no—
16#533×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151—22no—
19#529×C151—22no—
20#529×C151C2212yes—
21#501×C151C2214yes—
22#491×C151C2212yes—
23#491×C151C2212yes—
24#489×C151C2214yes—
25#487×C151—22no—
26#484×C151—22no—
27#481×C151—22no—
28#475×C151—22no—
29#474×C151—22no—
30#432×C151C2212yes—
31#419×C151—22no—
32C4×M16×C151C2211yescharacteristic
33#330×C151C2212yes—
34#330×C151C2214yes—
35#330×C151C2212yes—
36#329×C151C2214yes—
37C22×Q8×C151—21no—
38C2×M16×C151—21no—
39C4⋊Q8×C151—22no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151—22no—
42C4⋊Q8×C151—22no—
43C4⋊Q8×C151D412yes—
44C4⋊Q8×C151C2312yes—
45#126×C151—22no—
46#126×C151—22no—
47#126×C151—22no—
48#126×C151—22no—
49#126×C151—22no—
50#125×C151—22no—
51#125×C151—22no—
52#125×C151—22no—
53#125×C151—22no—
54#125×C151C2311yescharacteristic
55#125×C151C2311yescharacteristic
56#125×C151C2312yes—
57#124×C151—22no—
58#124×C151—22no—
59#124×C151C2312yes—
60#123×C151—22no—
61#123×C151—22no—
62#123×C151—22no—
63#123×C151—22no—
64#123×C151—22no—
65C22⋊Q8×C151—22no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151D412yes—
73#121×C151—22no—
74#121×C151—22no—
75#121×C151D412yes—
76C4×Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151D412yes—
79C4×D4×C151—22no—
80C4×D4×C151—22no—
81C4×D4×C151D412yes—
82#117×C151—22no—
83#117×C151—22no—
84#117×C151D412yes—
85C2×C4⋊C4×C151—22no—
86C2×C42×C151—22no—
87C2×C42×C151C2311yescharacteristic
88#107×C151—24no—
89#106×C151—24no—
90C4⋊C8×C151—22no—
91#103×C151—24no—
92#103×C151—24no—
93#103×C151—24no—
94#102×C151—24no—
95C22⋊C8×C151—22no—
96#97×C151C2312yes—
97#97×C151C2314yes—
98C4×C8×C151—21no—
99C2×Q8×C151—22no—
100C2×Q8×C151—22no—
101C2×Q8×C151—22no—
102C2×Q8×C151—44no—
103C2×Q8×C151—41no—
104C2×Q8×C151C2×D412yes—
105C2×D4×C151—22no—
106C2×D4×C151—22no—
107C2×D4×C151C2×D412yes—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—41no—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D412yes—
114M16×C151—42no—
115C2×C8×C151—22no—
116C2×C8×C151—24no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—42no—
132C4⋊C4×C151C2×D412yes—
133C4⋊C4×C151C2×D412yes—
134C4⋊C4×C151C2×D412yes—
135C4⋊C4×C151C2×D412yes—
136C22⋊C4×C151—22no—
137C22⋊C4×C151—22no—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—22no—
141C22⋊C4×C151—22no—
142C22⋊C4×C151—22no—
143C22⋊C4×C151—22no—
144C22⋊C4×C151—22no—
145C22⋊C4×C151—22no—
146C42×C151—22no—
147C42×C151—22no—
148C42×C151—22no—
149C42×C151—22no—
150C42×C151C2×D411yescharacteristic
151C42×C151C2×D412yes—
152C42×C151C2411yescharacteristic
153C23×C151—22no—
154C23×C151#12011yescharacteristic
155Q8×C151—42no—
156Q8×C151—44no—
157Q8×C151—82no—
158Q8×C151—82no—
159Q8×C151—82no—
160D4×C151—42no—
161D4×C151—82no—
162D4×C151—82no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—42no—
170C2×C4×C151—44no—
171C2×C4×C151—42no—
172C2×C4×C151—82no—
173C2×C4×C151—82no—
174C2×C4×C151—82no—
175C2×C4×C151#12012yes—
176C2×C4×C151#12011yescharacteristic
177C2×C4×C151C22×D411yescharacteristic
178C2×C4×C151C22×D412yes—
179C8×C151—44no—
180C8×C151—42no—
181C22×C151—21no—
182C22×C151—22no—
183C22×C151—42no—
184C22×C151—42no—
185C22×C151—42no—
186C22×C151C2×#12011yescharacteristic
187C4×C151—21no—
188C4×C151—22no—
189C4×C151—22no—
190C4×C151—42no—
191C4×C151—42no—
192C4×C151—42no—
193C4×C151—42no—
194C4×C151—42no—
195C4×C151—82no—
196C4×C151#45412yes—
197C2×C151—41no—
198C2×C151—82no—
199C2×C151C2×#45411yescharacteristic
200C2×C151#302212yes—
201#19005C15111yesmaximal, characteristic, direct product factor, Sylow
202C151#1900511yescharacteristic, direct product factor, Sylow
203#3531C2×C15111yescharacteristic
204#3239C2×C15112yescomplemented
205#3139C2×C15111yescharacteristic, complemented
206#1664C2×C15114yescomplemented
207#1663C2×C15112yescomplemented
208#1662C2×C15112yescomplemented
209#1537C2×C15111yescharacteristic, complemented
210#1529C2×C15112yescomplemented
211#564C22×C15111yescharacteristic
212#563—22no—
213#563—22no—
214#563C22×C15112yes—
215#562—22no—
216#562C22×C15111yescharacteristic
217#533—22no—
218#533C22×C15111yescharacteristic
219C2×C4⋊Q8C22×C15111yescharacteristic
220#529—22no—
221#529—22no—
222#529C22×C15112yes—
223#501C22×C15114yes—
224#491C22×C15112yes—
225#491C22×C15112yes—
226#489C22×C15114yes—
227#487—22no—
228#484—22no—
229#481—22no—
230#475—22no—
231#474—22no—
232#432C22×C15112yes—
233#419—22no—
234C4×M16C22×C15111yescharacteristic
235#330C22×C15112yes—
236#330C22×C15112yes—
237#330C22×C15114yes—
238#329C22×C15114yes—
239C22×Q8—21no—
240C2×M16—21no—
241C4⋊Q8—22no—
242C4⋊Q8—22no—
243C4⋊Q8—22no—
244C4⋊Q8—21no—
245C4⋊Q8D4×C15112yes—
246C4⋊Q8C23×C15112yes—
247#126—22no—
248#126—22no—
249#126—22no—
250#126—22no—
251#126—22no—
252#125—22no—
253#125—22no—
254#125—22no—
255#125—22no—
256#125C23×C15112yes—
257#125C23×C15111yescharacteristic
258#125C23×C15111yescharacteristic
259#124—22no—
260#124—22no—
261#124C23×C15112yes—
262#123—22no—
263#123—22no—
264#123—22no—
265#123—22no—
266#123—22no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8D4×C15112yes—
275#121—22no—
276#121—22no—
277#121D4×C15112yes—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×Q8D4×C15112yes—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4D4×C15112yes—
284#117—22no—
285#117—22no—
286#117D4×C15112yes—
287C2×C4⋊C4—22no—
288C2×C42—22no—
289C2×C42C23×C15111yescharacteristic
290#107—24no—
291#106—24no—
292C4⋊C8—22no—
293#103—24no—
294#103—24no—
295#103—24no—
296#102—24no—
297C22⋊C8—22no—
298#97C23×C15112yes—
299#97C23×C15114yes—
300C4×C8—21no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—44no—
305C2×Q8—41no—
306C2×Q8C2×D4×C15112yes—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4C2×D4×C15112yes—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4C2×D4×C15111yescharacteristic
315C22×C4C2×D4×C15112yes—
316M16—42no—
317C2×C8—22no—
318C2×C8—24no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—42no—
334C4⋊C4C2×D4×C15112yes—
335C4⋊C4C2×D4×C15112yes—
336C4⋊C4C2×D4×C15112yes—
337C4⋊C4C2×D4×C15112yes—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42C2×D4×C15111yescharacteristic
353C42C2×D4×C15112yes—
354C42C24×C15111yescharacteristic
355C23—22no—
356C23#120×C15111yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—82no—
360Q8—82no—
361Q8—82no—
362D4—42no—
363D4—82no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4#120×C15112yes—
378C2×C4#120×C15111yescharacteristic
379C2×C4C22×D4×C15111yescharacteristic
380C2×C4C22×D4×C15112yes—
381C8—42no—
382C8—44no—
383C22—21no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22C2×#120×C15111yescharacteristic
389C4—21no—
390C4—22no—
391C4—22no—
392C4—42no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—82no—
398C4#454×C15112yes—
399C2—41no—
400C2—82no—
401C2C2×#454×C15111yescharacteristic
402C2#3022×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3531×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3239×C151C2semidirect
3. #3139×C151C2semidirect
4. #1664×C151C2semidirect
5. #1663×C151C2semidirect
6. #1662×C151C2semidirect
7. #1537×C151C2semidirect
8. #1529×C151C2semidirect
201. #19005C151direct (N × H)
202. C151#19005direct (N × H)
204. #3239C2×C151semidirect
205. #3139C2×C151semidirect
206. #1664C2×C151semidirect
207. #1663C2×C151semidirect
208. #1662C2×C151semidirect
209. #1537C2×C151semidirect
210. #1529C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3531×C1512
#3239×C1512
#3139×C1512
#1664×C1512
#1663×C1512
#1662×C1512
#1537×C1512
#1529×C1512
#19005151